Controllability, stability and stabilizability of distributed parameter systems.

Abstract

In this thesis the question of stabilization of perturbed (or uncertain) infinite dimensional linear systems is considered. First, we identify the class of perturbations for which the system remains controllable thereby stabilizable by the same feedback law as for the nominal system. That is, sufficient conditions are presented that guarantee stabilizability of the perturbed system given that the unperturbed system has similar properties. Secondly, we present a methodology for designing feedback controllers such that the feedback system is stable. It is shown that exponential stability can be achieved by choice of suitable additional state feedback controls even in the presence of unbounded and nonlinear perturbations. Both deterministic and stochastic systems are considered. Finally, we apply these stabilization results to a simplified SCOLE model proposed by NASA. Numerical simulations are carried out to illustrate the impact of perturbations on the performance of the space structures and the effectiveness of the stabilizing control.